Here is a link to Ted Hildebrant’s article in the Grace Theological Journal 9.1 (1988) 3-19, Proverbs 22:6a; To Train Up A Child? which analyses what “To Train Up A Child” really means.
Here is a short quote from the intro:
Careful consideration of lexical and contextual factors suggests that “train up a child in the way he should go” needs to be reexamined. The verb “to train” really refers to a bestowal of status and responsibility. The noun translated “child” denotes the status of a late adolescent rather than a child. “In the way he should go” is best understood as “according to what is expected.” The original intent then of this verse addresses a late adolescent’s entrance into his place in adult society.
As he did not study the word for Rod, this article does not change his ideas about spanking. He does, however, come to the conclusion that the verse does not advocate early childhood training. He also reminds us that it is a Proverb, not a promise, which is something to keep in mind.
His final conclusion is this:
The parent must not violate the adolescent’s personhood by authoritarian domination, permissive allowance of immaturity, or overprotection from the consequences of his actions.
I must make note of the fact that his Hebrew words were transliterated Right to Left so that they read, “backwards” for us. If you want to read a better version of this article, you may read it here, but you will have to subscribe to the site first.